CBSE Class 6 Mathematics Basic Geometrical Concepts Worksheet Set 10

Q1 : Brain Teasers:-

Question 1. Diameter of the circle is ________ chord. (longest/shortest)
Answer: longest
In simple words: The diameter passes through the center, making it the longest chord in a circle.

Exam Tip: Remember that any chord passing through the center is a diameter and is the maximum possible distance between two points on a circle.

Question 2. A quadrilateral is______ sided polygon. (two/three/four)
Answer: four
In simple words: A quadrilateral is a closed figure made of four straight line segments.

Exam Tip: The prefix 'quad' means four, which helps you easily remember the number of sides.

Question 3. A polygon is a _________________ made up of entirely line segments.(open curve / closed curve)
Answer: closed curve
In simple words: A polygon must be completely closed and bounded by straight line segments.

Exam Tip: If any shape has an opening or is made of curved lines, it cannot be classified as a polygon.

Question 4. Line segment has _______ end points. (one / three)
Answer: two (Note: The source options list one/three, but the mathematically correct answer is two. A line segment has two distinct end points.)
In simple words: A line segment starts at one point and ends at another, giving it exactly two endpoints.

Exam Tip: Unlike a line (which extends infinitely in both directions) or a ray (which has one endpoint and extends infinitely in one direction), a line segment has a fixed, measurable length.

Question 5. A figure having no vertex & edges is ______. (sphere/triangle)
Answer: sphere
Note on source options: A sphere is a 3D surface, while a triangle is 2D. Strictly speaking, a sphere has no vertices and no edges, whereas a triangle has 3 vertices and 3 edges.
In simple words: A sphere is completely curved and smooth, so it does not have any sharp corners (vertices) or straight lines (edges).

Exam Tip: Always distinguish between 2D shapes (like triangles) and 3D shapes (like spheres) when counting vertices and edges.

Q2 : Define the following terms with figure…

Question 1. Point
Answer: A point is a fine dot made by a sharp pencil on a piece of paper. It determines a location and has no length, breadth, or thickness.

In simple words: A point is just a dot that shows an exact position.

Exam Tip: Always represent a point with a capital letter, such as point A.

Question 2. Geometry
Answer: Geometry is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. The word is derived from Greek words 'geo' (earth) and 'metron' (measure).
In simple words: Geometry is the study of shapes, sizes, lines, and angles around us.

Exam Tip: Geometry helps in measuring land, designing buildings, and understanding spatial relationships.

Question 3. Concurrent lines
Answer: Three or more lines in a plane are said to be concurrent if they all pass through the same single point. That common point is called the point of concurrency.

In simple words: Concurrent lines are multiple straight lines that intersect at one exact point (Point P).

Question 4. Ray
Answer: A ray is a portion of a line that starts at a given point (endpoint) and goes on endlessly in one direction.

In simple words: A ray is like a beam of light starting from a source and traveling infinitely in one direction.

Exam Tip: When naming a ray, always write the starting endpoint first, e.g., ray AB.

Question 5. Clarifies the difference between line segment and line.
Answer: - A line segment has two fixed endpoints and has a definite, measurable length.
- A line has no endpoints, extends endlessly in both directions, and cannot be measured.
In simple words: A line segment stops at both ends, whereas a line goes on forever in both directions.

Exam Tip: Use a ruler to measure a line segment, but remember that a line is an abstract concept that cannot be fully drawn on paper.

Q3 : Draw a circle and draw its…..

Question 1. radius
Answer: A radius is a line segment connecting the center of the circle to any point on its boundary.

In simple words: The radius is the distance from the center O to point A on the edge of the circle.

Exam Tip: All radii of the same circle are equal in length.

Question 2. diameter
Answer: A diameter is a line segment passing through the center with its endpoints on the circle.

In simple words: The diameter is a straight line passing through the center that divides the circle into two equal halves.

Exam Tip: Diameter is always twice the length of the radius (\(\text{Diameter} = 2 \times \text{Radius}\)).

Question 3. chord
Answer: A chord is a line segment joining any two points on the circumference of a circle.

In simple words: A chord is a line segment connecting two points on the circle's edge without necessarily passing through the center.

Exam Tip: The diameter is the longest chord of a circle.

Question 4. interior pointA, pointB
Answer: Points located inside the region bounded by the circle.

In simple words: Points A and B lie inside the circle.

Exam Tip: Interior means inside the boundary, whereas exterior means outside the boundary.

Question 5. Its Centre O
Answer: The fixed point from which all points on the circle are equidistant.

In simple words: Centre O is the exact middle point of the circle.

Exam Tip: The center is always used as the reference point for naming and drawing circles.

Question 4. What is the difference between vertices and corners of a figure?
Answer: In elementary geometry, the terms 'vertex' (plural: vertices) and 'corner' are often used interchangeably to describe a point where two or more straight line segments meet. Strictly speaking: - A vertex is a precise mathematical point of intersection of edges in a polygon or polyhedron. - A corner is a more general descriptive term used for any angular bend or intersection in 2D or 3D shapes.
In simple words: Both refer to the sharp meeting point of lines, but 'vertex' is the formal mathematical term.

Exam Tip: Use the word 'vertex' in formal geometry problems (e.g., vertices of a triangle).

Question 5. What is Data?
Answer: Data is a collection of facts, numbers, measurements, or observations gathered together for information, analysis, or reference.
In simple words: Data is raw information or facts collected about something.

Exam Tip: Data can be numerical (quantitative) like marks, or descriptive (qualitative) like eye color.

Question 6. What is pictorial representation of data and why it is needed?
Answer: Pictorial representation of data is the method of displaying numerical information using pictures, symbols, bar graphs, or pictographs. It is needed because: 1. It makes raw data easy to understand at a single glance. 2. It highlights comparisons and trends much faster than numbers alone. 3. It makes data interpretation interesting and accessible to everyone.
In simple words: Showing data with pictures makes it much easier to read and understand quickly.

Exam Tip: Always include a proper key or legend when drawing pictographs or bar graphs.

Question 7. Draw two of each: Closed curve and open curve
Answer:
Closed Curves: Figures that start and end at the same point without any breaks (e.g., Circle, Triangle).
Open Curves: Figures that have separate starting and ending points (e.g., S-shape, Wave line).

In simple words: A closed curve loops back on itself, while an open curve does not.

Exam Tip: Check if you can trace the path back to the starting point without lifting your pencil to confirm if it is closed.

Question 8. The total number of children in 20 families of a locality are give below. 2 2 3 2 1 3 3 2 2 1 2 2 3 1 2 1 1 3 2 2. Represent this information in a frequency distribution table.
Answer:
Let us count the frequency of each number of children (1, 2, and 3):
- Number of children = 1 appears 5 times.
- Number of children = 2 appears 10 times.
- Number of children = 3 appears 5 times.
Total families = \(5 + 10 + 5 = 20\).
Frequency distribution table:

In simple words: Count how many times each number appears and record it using tally marks and numbers.

Exam Tip: Always verify that the sum of all frequencies matches the total number of observations given in the problem.

Question 9. Number of students of a class who can sing, swim, dance, paint, draw are as follow : Sing - 20, Dance - 24, Draw - 8, Swim - 12, Paint - 16. Choose a symbol to represent the given information through a pictograph.
Answer:
Let us choose a symbol representing students. Let symbol \(\bigstar\) represent 4 students (since 4 is the HCF of 20, 24, 8, 12, 16).
- Number of symbols for Sing = \(\frac{20}{4} = 5\) symbols (\(\bigstar \bigstar \bigstar \bigstar \bigstar\))
- Number of symbols for Dance = \(\frac{24}{4} = 6\) symbols (\(\bigstar \bigstar \bigstar \bigstar \bigstar \bigstar\))
- Number of symbols for Draw = \(\frac{8}{4} = 2\) symbols (\(\bigstar \bigstar\))
- Number of symbols for Swim = \(\frac{12}{4} = 3\) symbols (\(\bigstar \bigstar \bigstar\))
- Number of symbols for Paint = \(\frac{16}{4} = 4\) symbols (\(\bigstar \bigstar \bigstar \bigstar\))

In simple words: Assign a symbol to represent a specific group of students (like 4 students per symbol) to draw the pictograph.

Exam Tip: Always state your scale clearly at the bottom or top of the pictograph (e.g., Scale: 1 symbol = 4 students).

Question 10. Name the common side of two triangles.
Answer: Line segment AD (or side AD)
In simple words: Side AD is shared between triangle ABD and triangle ACD.

Exam Tip: When naming a line segment, you can write AD or DA interchangeably.

Question 11. What type of figure this is?
Answer: The given figures consist of various 2D and 3D geometric shapes: 1. 2D arrow shape (cross/arrow polygon) 2. Triangle (2D polygon) 3. Quadrilateral / Rhombus or parallelogram (2D polygon) 4. Trapezium / Trapezoid (2D polygon) 5. Cuboid / Cube (3D solid figure) 6. Arrow / directional chevron (2D polygon) 7. Quadrilateral / Parallelogram (2D polygon) 8. Wave ribbon / Open or closed curved banner (2D figure)
In simple words: The set contains a mix of 2D flat geometric shapes and 3D solid figures.

Exam Tip: Learn to properly classify shapes into polygons, curves, 2D flat shapes, and 3D solids.